(Adapted from NYEngage) Use similar triangles to find the length of the altitude

The type of ticket that must have been sold are 100 adults and 400 students

Also, they were short by $360

Given that tickets are sold for adults and students

Let d = adults

Let s = students

So, we have

6.5d + 3.5s = 2050

d + s = 500

When solved graphically, we have

d = adults = 100

s = students = 400

Here, we have

s = 3d

s + d = 480

So, we have

4d = 480

Evaluate

d = 120

s = 360

So, we have

Total = 6.5 * 120 + 3.5 * 260

Total = 1690

Difference = 2050 - 1690

Evaluate

Difference = 360

They were short by $360

Read more about system of equations at

https://brainly.com/question/13729904

#SPJ1

Answer:

Step-by-step explanation:

A. Variability means the spread of the range for between the 3rd and 1st quartile meaning the actual box.  The actual box is wider with South Middle so the difference is greater and therefore greater variability

B. North Middle has greater distance in general because the box has bigger numbers.  That's where the majority of the kids are, so in general North Middle has kids that are further away  

If the width of the rectangle is 21 inches, the length is 24.5cm and the area is 372cm²

A  rectangle is described as a quadrilateral with four right angles.

suppose we have the width of rectangle = 21 inches

therefore:

( x + 0.5) = 21

x = 20.5

Area of rectangle =  we multiply the length of the rectangle by the width of the rectangle.

 2x² + 9x + 4

Area of rectangle = 2(11.5)² + 9(11.5) + 4

=  372cm²

length of rectangle = x + 4

length of rectangle= 20.5 + 4

length of rectangle = 24.5cm

Learn more about Area of rectangle at:

https://brainly.com/question/2607596

#SPJ1

Answer: BC = 8.94

Step-by-step explanation:

      Since this is a right triangle, we can use the Pythagorean theorem. a and b are the triangle legs and c is the hypotenuse.

a² + b² = c²

19² + b² = 21²

361 + b² = 441

b² = 80

b = [tex]\sqrt{80}[/tex]

b ≈ 8.94

BC = 8.94

The graphs to match each inequality to its solution are added as an attachment

Analyzing the inequalities from the question, we have the following explanations

Next, we match the number lines and the inequalities

See attachment for number lines

Read mroe about inequalities at

https://brainly.com/question/30390162

#SPJ1

As a result, twenty-five percent of the responses were not cataloged in the table.

To begin with, discover the amount of replies that failed to be noted:

Complete Responses - Documented Responses = Unrecorded Responses

200 - 150 = 50

Next, estimate the proportion of responses not represented in the table:

(Unrecorded Responses / Total Responses) * 100%

(50 / 200) * 100% = 0.25 * 100% = 25%

As a result, twenty-five percent of the responses were not cataloged in the table.

Read more about algebra here:

https://brainly.com/question/22399890

#SPJ1

Cecilia collected a total of 200 service responses for her study. She noticed that only 150 responses were recorded in the table. What percent of the responses were not recorded in the table?

The probability of winning the minimum prize is approximately 0.00014

To calculate the probability of winning this minimum prize, we need to first find out the total number of possible combinations of numbers that can be drawn.

There are 56 white balls, and 5 balls are drawn from them, so the total number of possible combinations of white balls is

56 choose 5 = 56! / (5! (56-5)!) = 3,819,816

There are 46 gold balls, and only 1 is drawn from them. Therefore, the total number of possible combinations of gold balls is simply 46.

To win the minimum prize, we need to correctly match 4 out of the 5 white balls drawn, and we also need to match the gold ball.

The number of ways to choose 4 white balls out of 5 is

5 choose 4 = 5! / (4! (5-4)!) = 5

So, the total number of ways to win the minimum prize is the product of the number of ways to choose 4 white balls and the number of ways to choose 1 gold ball

Total number of ways to win the minimum prize = 5 × 46 = 230

Therefore, the probability of winning the minimum prize is

Probability = number of ways to win the minimum prize / total number of possible combinations

Probability = 230 / (3,819,816 × 46) = 0.00014

Learn more about Probability here

brainly.com/question/11234923

#SPJ4

Answer:Width=5, Length=10

Step-by-step explanation:

You can solve this by using a variable, x, and assigning it to the value that is the width.

Since the perimeter of a rectangle is the width times two plus the length times two, you can use an equation that looks like this:

(image shown)

This will give you the value of X, the width, and you can multiply this value by 2 to get the length.

Answer:

10 cm

Step-by-step explanation:

The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length and w is the width1. We know that the perimeter of this rectangle is 30 cm. So we can write:

2(2w + w) = 30

Simplifying this equation gives:

6w = 30

Therefore:

w = 5

So the width of the rectangle is 5 cm and its length is twice as long as its width which means it’s 10 cm.

Answer:

Height 15 feet

Base 12 Feet

Step-by-step explanation:

The formula to find the area of a triangle is A= (0.5) x base x height, so if the area is 90 then before it was halved it must be 180 so the base x height must equal 180 and the only number that equal 180 when multiplied with a difference of 3 between them is (15,12) so thats are answer. I know this is right because if I put it through the area formula I get 90.

A=(.5) x 12 x 15

A=(.5) x 180

A= 90

Answer:

a)1/12

b)3/4

c)5/12

d)2/3

Step-by-step explanation:

let chocolate bar be C

let fruit chew be F

let Pack of buble gum be =B

1let sour Candie be S

C=4

F=4

B=1 pack

S=3

T=4+4+1+3=12

a) 1/12

b)9/12=3/4

c)4/12+1/12=1/3+1/12=5/12

d)8/12=2/3

The number of  hours it would take 6 pipes to fill 1/4 of the lake is 4.5 hours

Given that

It takes 4 of the pipes 12 hours to fill the lake.

This means that

Rate = 12 hours/4 pipes

So, we have

Rate = 3 hours/ pipe

For 6 pipes to fill 1/4 of the lake. we have

Time = 3 hours *6 * 1/4

Evalaute

Time = 4.5 hours

Hence, the time taken is 4.5 hours

Read more abuot rate at

https://brainly.com/question/24178013

#SPJ1

The angle in standard position is  150°

The angle of any position (x, y) on a graph is given by Ф = tan⁻¹(y/x).

Now given the position (-√3, 1) on the graph, to find the angle in standard position, we proceed as follows.

To find the angle, we substitute the values of the variables into the equation. so, we have that

Ф = tan⁻¹(y/x)

Given that

Ф = tan⁻¹(y/x)

Ф = tan⁻¹(1/-√3)

= tan⁻¹(-1/√3)

= 180° - tan⁻¹(1/√3)

= 180° - 30°

= 150°

So, the angle is  150°

Learn more about angle in standard position here:

https://brainly.com/question/30750289

#SPJ1

Answer:

In geometry, formal definitions are formed using other defined words or terms. There are, however, three words in geometry that are not formally defined. These words are point, line and plane, and are referred to as the " three undefined terms of geometry ".

Step-by-step explanation:

Answer:  

Step-by-step explanation:

Step-by-step explanation:

there are 2 formulas to calculate the length of a chord, depending on what pieces of information we have.

here now we have the length of the chord, which we need to find the radius, which we need to find the angle at the center.

chord length = 2×sqrt(r² - d²)

chord length = 2×r×sin(c/2)

r is the radius, d is the distance of the chord from the center of the circle, c is the angle of the chord at the center of the circle.

20 =2×sqrt(r² - 12²) = 2×sqrt(r² - 144)

10 = sqrt(r² - 144)

100 = r² - 144

244 = r²

r = 15.62049935... cm

20 = 2×r×sin(c/2) = 2×15.62049935...×sin(c/2)

10 = 15.62049935...×sin(c/2)

sin(c/2) = 10/15.62049935... = 0.6401844...

c/2 = 39.80557109...°

c = 79.61114218...° ≈ 79.6°

(a) the angle subtended by the chord at the center of the circle is about 79.6°.

(b)

the arc length of a segment is 2pi×r × c/360

in our case

2×3.142×15.62049935...×79.61114218.../360 =

= 21.70713182... cm

the whole perimeter of the segment is then arc length + chord length =

= 21.70713182... + 20 = 41.70713182... ≈ 41.7 cm

the perimeter of the minor segment cut off by the chord is about 41.7 cm.

Answer:

The parrot is 48 years old and knows 76 words.

Step-by-step explanation:

The outlier is far away from all the other points on the y-axis and the x-axis.

Answer:

The answer is d) 2/c.

Explanation :

If one of the zeroes of cubic polynomial x^3+ax^2+bx+c is 2, then the product of the other two zeroes can be found by dividing the polynomial by (x-2), which gives:

x^3+ax^2+bx+c = (x-2)(x^2+(a+2)x+(c-2a))

We can solve the quadratic equation x^2+(a+2)x+(c-2a) to find the other two zeroes. By Vieta's formulas, the product of the roots of a quadratic equation ax^2+bx+c=0 is c/a. Therefore, the product of the other two zeroes is:

pq = (c-2a)/1 * 1/(a+2) = (c-2a)/(a+2)

Substituting the value of c/2a from the cubic polynomial gives:

pq = (c-2a)/(a+2) = (2c-4a)/(2a+4) = -2(c/2a) + 2

Therefore, the answer is d) 2/c.

With a significance level of 0.05 for a one-tailed test, the critical value is 1.761. Since -1.86 is less than -1.761, we reject the null hypothesis.

To test for significant increases in average domestic business charges over a one-year period, you can use a paired-sample t-test.

This is good because the two sets of observations (current year and previous year) are paired on the same flight.

The null hypothesis (H0) states that the average domestic fares for business travel are not significantly different from the previous year.

The alternative hypothesis (Ha) indicates that average domestic fares for business travel will increase significantly this year compared to the previous year.

This can be written as:

H0:

µd = 0

teeth:

µd > 0

where μd is the population mean of the differences in domestic fares between the current year and the previous year.

To do the test, to begin with, calculate the contrast between the residential passages for the current year and the past year.

At that point calculate the mean and standard deviation of these contrasts.

 d = (558-219) + (417-312) + ... + (348-369) / 15

= -15.2

s = sqrt([(558-219+15.2)^2 + ... + (348-369+15.2)^2] / (15-1))

= 134.8

The t-statistic for the test is

t = (d - 0) / (s / sqrt(n))

= (-15.2 - 0) / (134.8 / square(15))

= -1.86

Using a one-sided test with 14 (n-1) degrees of freedom and a t table with a significance level of 0.05, the critical value is 1.761. -1.86 is less than -1.761, so we reject the null hypothesis.

It can in this manner be concluded that there's adequate proof to back the claim that the normal household airfare for trade travel has expanded essentially over the years. 

learn more about the null hypothesis.

brainly.com/question/28920252

#SPJ4

Leroy's total employment compensation last year was $46,650. Hence, the correct answer is option a, $46,650.

To find Leroy's total employment compensation, we need to consider his total job benefits and his total job expenses for traveling and professional development.

Leroy's total job benefits last year were $50,150. His total job expenses for traveling and professional development were $3,500. To calculate his total employment compensation, we need to subtract the job expenses from the job benefits.

Total employment compensation = Total job benefits - Total job expenses
Total employment compensation = $50,150 - $3,500
Total employment compensation = $46,650

The correct option is a. $46650.

To know more about compensation here:

https://brainly.com/question/29616045

#SPJ1

The two forms of writing that have a similar purpose of entertaining an audience are as follow,

A short story

An epic poem

Short stories and epic poems are both forms of literature.

That are designed to entertain readers through the use of compelling characters, interesting plots, and vivid descriptions.

A news article, a book report, and do-it-yourself instructions have different purposes.

A news article is designed to inform readers about current events.

The current event may relates to day day life or to the nature.

A book report is designed to summarize and analyze a book.

IN book report mostly famous books are included to spread the awareness about the book.

And do-it-yourself instructions are designed to provide step-by-step guidance on how to complete a task.

Do -t - yourself is consider as a individual task.

learn more about writing here

brainly.com/question/5142991

#SPJ4

Answer:

13*

Step-by-step explanation:

Use the Pythagorean theorem.

a=1

b=x

c=13

so, [tex]1^2 + x^2 = 13^2[/tex]

[tex]x^2 = 169 - 1 = 168[/tex]

[tex]x = \sqrt{168}[/tex]

 [tex]\sqrt{168} = 12.961481396815720461931934872176[/tex] = 13

*If we round to the nearest tenth, we get 13. Because of this rounding, the other leg is the hypotenuse, but it is actually different.

The proof is completed using the properties of equality

The two column proof is completed as below

Statement                                              Reason

angle 2 ≅ angle 4                                  Given

angle 1 + angle 2 = 90 deg                   definition of right triangle

angle 3 + angle 4 = 90 deg                  definition of right triangle

angle 1 + angle 2 = angle 3 + angle 4  substitution property of equality

angle 1 + angle 4 = angle 3 + angle 4  substitution property of equality

angle 1 = angle 3                                   addition property of equality

Learn more about two column proof at

https://brainly.com/question/18286984

#SPJ1

Answer:

7/14 in simplest form is 1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

The length of line AC of the given quadrilateral ABCD would be = 13.7cm

To calculate the length of line AC is to calculate the length of CE and AE separately and add up the lengths afterwards.

The length of CE can be calculated using Pythagorean formula;

That is C² = a² +b²

where C = 8cm

a = 5cm

b = CE = ?

b² = 8²-5²

b = 64-25

b² = 39

b =√39

b = 6.2

For AE;

b² = AE = 9²-5²

= 81-25

= 56

b = √56

= 7.5

Therefore the length of AC = 6.2+7.5 = 13.7cm

Learn more about length here:

https://brainly.com/question/28108430

#SPJ1

To compare the two running times, we need to express them in the same units. We can convert Sylvester's time to seconds by multiplying by 60:

Sylvester: 4 minutes x 60 seconds/minute = 240 seconds

Lenworth: 4 minutes 12 seconds = 4 x 60 + 12 = 252 seconds

Now we can find the ratio of Lenworth's time to Sylvester's time:

Lenworth/Sylvester = 252/240 = 21/20

So the ratio of Lenworth's time to Sylvester's time is 21:20.

The height of the metal prism is 1/10 times the height of the tank.

The height h of the metal prism is calculated as follows;

Since the tank is half-filled with water, the height of the water in the tank is H/2.

let the height of the prism = h

Volume of the rectangular tank + volume of prism = total volume

1/2 x L x W x H + L x W x h = 3/5 x L x W x H

H/2  + h = 3H/5

h = 3H/5 - H/2

h = H/10

Therefore, the height of the metal prism is 1/10 times the height of the tank.

Learn more about height of prism here: https://brainly.com/question/27677501

#SPJ4

Answer:

Step-by-step explanation:

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, to find the perimeter of the triangle with sides a = 24, b = 45, and c = ?, we need to add up the lengths of the known sides:

Perimeter = a + b + c

Plugging in the values, we get:

Perimeter = 24 + 45 + c

Simplifying, we get:

Perimeter = 69 + c

We still need to find the length of the third side, c. However, we can use the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words:

a + b > c

24 + 45 > c

69 > c

Therefore, we know that c must be less than 69.

On the other hand, we can also use the fact that the difference between the lengths of any two sides of a triangle must be less than the length of the third side. In other words:

|a - b| < c

|24 - 45| < c

21 < c

Therefore, we know that c must be greater than 21.

Putting these two inequalities together, we have:

21 < c < 69

So the perimeter is:

Perimeter = 69 + c

And we know that:

21 < c < 69

Therefore, we can say that the perimeter is somewhere between:

69 + 21 = 90

and

69 + 69 = 138

Rounding to the nearest tenth, we get:

Perimeter ≈ 90.0 - 138.0

Therefore, the perimeter is somewhere between 90.0 and 138.0, depending on the actual length of the third side, c.

Answer:

a)  $16,122

b) $4,246

c) $112,357

Step-by-step explanation:

What is depreciation

We should calculate the depreciation using the declining balance method
This uses the technique of computing the depreciation on the previous year's depreciated value

As an example
If the original cost is $100 and depreciation rate is 10%( 0.10 in decimal)

Depreciation Year 1 = 100 x 0.10 = $10

Depreciated value at end of year 1 = 100 - 10 = $90

For the second year, the depreciation amount is computed on $90
= 90 x 0.10 = $ 9

Depreciated amount at end of year 2 = 90 - 9 = $81

The depreciated value of an asset valued at $A at time of purchase at a depreciation rate of r (in decimal) for n years is given by the formula
A' = A(1 - r)ⁿ

We are given
A = $34,145
r = 8/100 = 0.08 therefore 1 - r = 1 - 0.08 = 0.92

a) Depreciated value after 9 years:
A' = 34145(0.92)⁹
    = 16121.95

Rounded to the nearest dollar that would be $16,122 ANSWER

b) Depreciated Value after 25 years

A' = 34145(0.92)²⁵

    = $4,246  rounded to the nearest dollar

c) Car's value after 50 years

At the end of 25 years, the Mustang has become a classic with a value of $4, 246

Then it starts to appreciate at the rate of 14% (0.14 in decimal)

The appreciated value each year after 25 years is given by
A'' = A'( 1 + r)ⁿ

where r is the rate of appreciation and n is the number of years

We are given r = 14% = 0.14

1 + r = 1.14

n = 25

A' = 4,246 the value after 25 years from purchase

Car value after 50 years = car value after 25 years appreciated for the next 25 years

= 4246(1.14)²⁵

= $112,357 rounded to the nearest $

So you can really make a killing after 25 years. As an interesting side note, the value of the car will reach the original value 16 years after 25 years or a total of 41 years after purchase

1. Identify the curve and the point: The curve is y = sec(x), and the point is (π/6, 2√3/3).

2. Calculate the derivative of the curve: The derivative of y = sec(x) is y' = sec(x)tan(x).

3. Evaluate the derivative at the given point: At x = π/6, we have y' = sec(π/6)tan(π/6). Since sec(π/6) = 2 and tan(π/6) = √3/3, we get y' = 2(√3/3) = 2√3/3.(4). Use the point-slope form of the line equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope (derivative).

5. Plug in the values: y - (2√3/3) = (2√3/3)(x - π/6). This is the equation of the tangent line to the curve y = sec(x) at the point (π/6, 2√3/3).

To know more about derivative click here

brainly.com/question/29096174

#SPJ11